JEE-Advanced 2015 (28/40)

Geometry Level 4

Suppose that \(\vec p, \vec q\) and \(\vec r\) are three non-coplanar vectors in \(\mathbb R^3\). Let the components of a vector \(\vec s\) along \(\vec p, \vec q \) and \(\vec r\) be 4, 3 and 5 respectively. If the components of this vector \(\vec s\) along \((-\vec p+\vec q+\vec r),(\vec p- \vec q +\vec r)\) and \((-\vec p -\vec q +\vec r)\) are \(x,y\) and \(z\) respectively, then find the value of \(2x+y+z\).

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